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Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of ki‐Strictly Pseudocontractive Mapping in Hilbert Spaces

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  • Haitao Che
  • Meixia Li
  • Xintian Pan

Abstract

We first extend the definition of Wn from an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of ki‐strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

Suggested Citation

  • Haitao Che & Meixia Li & Xintian Pan, 2012. "Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of ki‐Strictly Pseudocontractive Mapping in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:416476
    DOI: 10.1155/2012/416476
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    References listed on IDEAS

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    1. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "An Iterative Method for Solving a System of Mixed Equilibrium Problems, System of Quasivariational Inclusions, and Fixed Point Problems of Nonexpansive Semigroups with Application to Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-30, February.
    2. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-28, September.
    3. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    4. Tanom Chamnarnpan & Poom Kumam, 2012. "Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed‐Point Problems, and Variational Inclusions with Application to Minimization Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Poom Kumam & Phayap Katchang, 2012. "A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "An Iterative Method for Solving a System of Mixed Equilibrium Problems, System of Quasivariational Inclusions, and Fixed Point Problems of Nonexpansive Semigroups with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. Tanom Chamnarnpan & Poom Kumam, 2012. "Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-29, March.
    8. Poom Kumam & Phayap Katchang, 2012. "A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-35, May.
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